18 Mr Greenhill, Complex Multiplication [Oct. 29, 



'i i — i J 2c J2i — c 



therefore 



c ' ic+l-j2c(l + i) 



_ i Ji 



1 



Jig' 

 1 + y 1 (a + xf(j3 + xY 



ic +V JiG{*-x)\P-xy 

 ■which proves the first part. 



We have then 



(1 -y) B = - (1 - ic)(i-l)(l-x){ic+x)(J- ic + xf, 

 (l+y)B = P(oi + xf{l3+x)\ 

 (ic- y)D = - {ic - 1) J2c (1 + x) (ic - x) {J~^ic - xf, 

 (ic+y)D = Q(a-x?{P-x)*- t 

 therefore (1 - y 2 ) (y 2 + c 2 ) D i 



=PQ (1 - i) J 2c (1 - icf (1 - x*) (a? +c 2 ) (a 2 - xj(^- xj(ic + x 2 f, 



(ll^)(f 2 +c 2 ) = W (1 " *"> ^ {1 - icY (a2 ~ X * m ~ x7 {iG + X * f 



2P 2 c (1 - icf (a 2 - Q 2 (/3 2 - xyjic + x*f ... 

 — Jyi ...(A). 



Again, since 

 +c 



1-3/= ' 1 + c +^ {(z* c - ^ 2 ) 2 -2icV-^ (1-^c) +(^c-^ 2 ) (1- ^-/c) 2 ^}, 



we have 



dy _i — l-t- c + ic 



x \d [4jc (*c - a? 2 ) + 4x J - ic (1 - ic) - {ic -3x*){l-J- icf] 

 + [(ic -xj- 2x z J-Tc (l-ic)+(ic-x*) (l-J-wfx] ~ 



0,00 



i — 1 + c + ic 



